Crystal rate limiting factors

This study showed that the overall crystallization processes for mor-denite, zeolite X, and zeolite A were similar. However, the physical properties of the crystallizing system determine the rate-limiting step for a particular zeolite synthesis. In the case of mordenite in which both the viscosity of the batch composition and the morphology of seed crystals were varied, it was observed that diffusion in the liquid phase was the ratedetermining step. For zeolite X the actual growth rate on the crystal-liquid interface was the rate-limiting factor as shown by identical conversion rates for the seeded and unseeded systems. For zeolite A in the system chosen, both processes influenced the conversion rate. 

Equation 9.30 describes a diffusion-controlled dissolution process (4). It is visualized that when solid drug particles are introduced to the fluids at the absorption sites, the drug promptly saturates the diffusion layer (Fig. 9.17). This is followed by the diffusion of drug molecules from the diffusion layer into the bulk solution, which is instantly replaced in the diffusion layer by molecules from the solid crystal or particle. This is a continuous process. Although it oversimplifies the dynamics of the dissolution process. Equation 9.30 is a qualitatively useful equation and clearly indicates the effects of some important factors on the dissolution and, therefore, the absorption rate of drugs. When dissolution is the rate-limiting factor in the absorption, then bioavailability is affected. These factors are listed in Table 9.4. 

Dissolution of a drug substance is controlled by several physicochemical properties, including solubility, surface area, and wetting properties. For insoluble compounds, dissolution is often the rate-limiting step in the absorption process. Knowledge ofthe dissolution rate of a drug substance is therefore very useful for formulation development. The appropriate dissolution experiments can help to identify factors that contribute to bioavailability problems, and also assist in the selection of the appropriate crystal form and/or salt form. Dissolution tests are also used for other purposes such as quality control and assisting with the determination of bioequivalence (Dressman et al., 1998). 

Various additional experiments have been done with different air-flow rates over the samples and different salt concentrations. In figure 7. we have plotted all pathways for the experiments performed with the various samples starting at initial concentrations of 1 and 3 M.In a few experiments indeed the boundary line of Pe 1 is followed. This indicates that the salt crystallization is indeed fast enough and is not a limiting factor that is, there are enough nucleation sites in this type of material and no supersaturation occurs. In contrast to the experiments for 3 M, it is possible to follow the Pe [Pg.157]

The metastable form which preferentially crystallizes could then transform to a more stable phase (i.e. zeolite Y - zeolite X or zeolite A - hydroxysodalite). Nucleation and growth rates would then become the limiting factors in determining how long this would take. For example, when synthesis conditions are chosen to produce zeolite A, the rate of hydroxysodalite formation is dependent on five variables. These variables and their effect on the conversion of zeolite A to hydroxysodalite are as follows ... 

As a melt is cooled below its liquidus (the equilibrium melting temperature of the crystalline phases), the nucleation rate is initially small because AG /T is large. Further cooling reduces AG jT until it approximately equals Q/T. At this temperature, the maximum nucleation rate occurs. Further cooling increases Q/T relative to AG /T that is, diffusion becomes the limiting factor, and nucleation eventually stops. Because the maximum nucleation rate often occurs at a lower temperature than the temperature at which the crystal growth rate is maximum, numerous nuclei can form. 

The kinetics of several well-known electrochemical reactions have been studied in the presence of an ultrasonic field by Altukhov et al. [142], The anodic polarization curves of Ag, Cu, Fe, Cd, and Zn in various solutions of HC1 and H2S04 and their salts were measured in an ultrasonic field at various intensities. The effect of the ultrasonic field on the reaction kinetics was found to be dependent on the mechanism of metal anodic dissolution, especially on the effect of this field on the rate-determining step of the reaction. The results showed that the limiting factor of the anodic dissolving of Cu and Ag is the diffusion of reaction products, while in the case of Fe it is the desorption of anions of solution from the anode surface, and at Cd the limiting factor is the rate of destruction of the crystal lattice. Similar results were obtained by Elliot et al. [ 143] who studied reaction geometry in the oxidation and reduction of an alkaline silver electrode. 

The kinetics for a solvent mediated phase transformation will be governed by the kinetics of dissolution, nucleation, and crystal growth. These rates will depend directly on the solvent and any step may be rate limiting. As discussed in earlier sections of this chapter, the solvent influences the nucleation rate and crystal growth rate via two factors 1) solute solubility and 2) specific solvent-solute interactions. The dissolution rate will also be solvent dependent as pharmaceutical materials generally exhibit a wide range of dissolution rates in different solvents. 

After this initial contact time, the nuclei have grown but, more importantly, (C — C,) has decreased, as the very high crystallization rate has consumed large quantities of exogeneous tartrate. In other words. A, i.e. the diffusion rate, is no longer the limiting factor, but rather the state of supersaturation (C — C,). As C tends towards Q, the situation in the wine approaches the theoretical solubility (S) of tartrate under these treatment conditions. Therefore, by the end of the treatment process, the crystallization rate is controlled more by thermodynamics than kinetics. 

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